Redshift ↔ Velocity/Distance mechanism

Model scope

The core arithmetic is correct under the stated low-z approximation and consistent units, but the specification needs review before release. It must define the wavelength conversion, exact H0 presets and units, validation constraints, and the precise meaning of velocity and distance. The honest label should explicitly state that v=cz and d=v/H0 are low-redshift approximations and that H0 is user-selectable and contested.

• v=cz is the correct first-order non-relativistic approximation only when z is much less than 1; it is not a general redshift-to-velocity formula.
• d=v/H0 is the low-redshift linear Hubble-law distance, not a general cosmological distance such as comoving, luminosity, or angular-diameter distance.
• The wavelength-input path is underspecified: it must explicitly define z=(observed_wavelength-rest_wavelength)/rest_wavelength.
• The exact selectable H0 values are not specified, and the result depends materially on that choice.

Units and conventions

• Redshift z is dimensionless.
• c is taken as 299792.458 km/s.
• H0 must be supplied in km/s/Mpc for d=v/H0 to return Mpc.
• Observed and rest wavelengths must use the same units; nanometers cancel in their ratio.
• The reported velocity is in km/s and the reported Hubble-law distance is in Mpc.
• The approximation assumes z is sufficiently small; z=0.1 is already only a low-redshift illustrative case, not a generally accurate cosmological-velocity calculation.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "z": 0.01,
    "H0_km_s_Mpc": 67.4,
    "c_km_s": 299792.458
  },
  "expected_outputs": {
    "velocity_km_s": 2997.92458,
    "distance_Mpc": 44.47959317
  },
  "working": "v = cz = 299792.458 km/s × 0.01 = 2997.92458 km/s. d = v/H0 = 2997.92458 km/s ÷ 67.4 km/s/Mpc = 44.47959317 Mpc."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The distance calculation is undefined when the user selects H0=0, and the specification provides no explicit high-redshift branch or threshold even though v=cz is only a low-z approximation. Wavelength-field reversal also produces a materially different signed result.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json